2020/10/31 by Abijith Krishnan, Ashvin Vishwanath, Hoi Chun Po
Materials Science · Mathematics · Physics and Astronomy · #Advanced Condensed Matter Physics #Condensed matter physics #Electron #Graphene research and applications #Invariant (physics) #Mathematics #Physics #Polarizability #Quantum #Quantum Hall effect #Quantum mechanics #Quantum phase transition #Theoretical physics #Topological Materials and Phenomena #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.104.085128
published as Phys. Rev. B 104, 085128 (2021) · 9+3 pages, 4 figures
arxiv created 2021/08/16 · openalex publication_date 2021/08/16 · arxiv updated 2021/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
Traditional ionic and covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum Hall effect systems, do not typically display such a commensuration. Instead, they can undergo a phase transition to a trivial insulator that preserves the electron filling. Nevertheless, in some crystalline insulators, termed filling-enforced quantum band insulators (feQBIs), electron filling can dictate nontrivial topology in the insulating ground state. Currently, little is known about the relation between feQBIs and conventional topological invariants. In this work, we study such relations for a particularly interesting example of a half-filling feQBI that is realized in space group 106 with spinless electrons. We prove that any four-band feQBI in space group 106 with filling 2 must have a nontrivial topological invariant, namely, the ℤ2 glide invariant, and thus must have a quantized magnetoelectric polarizability \ensuremathθ=\ensuremathπ. We thus have found a three-dimensional example where electron filling and band topology are tied. Such a locking raises intriguing questions about the generality of the band-inversion paradigm in describing the transition between trivial and topological phases.